Generalizing Hartogs' Trichotomy Theorem

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A celebrated argument of F. Hartogs (1915) deduces the Axiom of Choice from the hypothesis of comparability for any pair of cardinals. We show how each of a sequence of seemingly much weaker hypotheses suffices. Fixing a finite number $k>1$, the Axiom of Choice follows if merely any family of $k$ cardinals contains at least one comparable pair.
8 pages with an appendix by Andreas Blass

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Logic, 03E25

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http://salesiana.dossiersoluciones.com/handle/123456789/158121

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0804.0673
 http://arxiv.org/abs/0804.0673

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arXiv